I've had occasion to correct the player number I had reported to the scorer, when I realized that I'd given it incorrectly. And over all the years and games I've officiated, I've had two inadvertent whistles. And I'm glad that I did the right thing by admitting and correcting my error(s).
I agree with those who've said that it has to be okay to do so, even though we consider the OP to be of greater import than an inadvertent whistle, or a case of reporting a foul on the wrong player of the same team.

For the one time in a career that this might happen, I'd be willing to take the hit for getting this fixed. If it happens more than that, then my assigner is going to have other concerns.

That is the proper way to think about this.

Here is your rule support for fixing this.

2-11-11 "A bookkeeping mistake may be corrected at anytime until the referee approves the final score."

Now you must understanding that an official telling the scorer what to record is part of the recordkeeping process. If the official mistakenly says "blue 32" instead of "white 32", the wrong team is not stuck with a foul for the rest of the game. If the official mistakenly says "red 41" instead of red "14", the wrong player isn't stuck with the foul for the rest of the game. Furthermore, what if an official says "green 34" while indicating the numbers "3" and then "5" with his hand(s)? These are all simple mistakes that humans make. There is no intent under the rules to improperly penalize a team when an official says something wrong.

Your situation is no different. You correctly observed the foul and made the decision on the court regarding which player to penalize. You just got confused and messed up during the reporting process (and didn't the needed help from your partner). There is no rule which mandates that the reporting process is binding. You may fix the bookkeeping aspect of the game whenever necessary.

Thank you, guys. I really appreciate the help.

+1 with Nevada

Prescribed mechanics
 

Bryan, I have a question about your mechanics at the spot of the foul. Did you move in toward the offender, state the jersey color and number and perhaps give a preliminary signal, or did you just go up with the fist and start to leave the area to report the foul?

Normally it goes whistle, first, wait and make sure the number of the players and that things are cool. , then go report the foul.

If you actually state the number at the spot, it can help avoid similar situations.

I'll give it a try... Thanks

Bryan, it is part of a definite procedure in officiating mechanics to be used when a foul occurs. It can never hurt and can only help. It is an important part of communication. Even so, I would say 90% of officials I observe here in my part of Ohio choose to skip it, setting themselves up for rare but potential embarrassing situations that are bound to happen eventually. Yours just did. Don't settle on just giving it a try. Make it a standard in your mechanics.